1. Calculate the daily work rate for Contractor P: 1/20 of the project per day. 2. Calculate the daily work rate for Contractor Q: 1/30 of the project per day. 3. Calculate their combined daily work rate: 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 of the project per day. 4. Calculate the work completed in the first 5 days by both contractors: 5 days * (1/12 project/day) = 5/12 of the project. 5. Calculate the remaining work: 1 - 5/12 = 7/12 of the project. 6. Calculate the time Contractor Q takes to complete the remaining work alone: (7/12 project) / (1/30 project/day) = (7/12) * 30 = 7 * (30/12) = 7 * (5/2) = 35/2 = 17.5 days. 7. Calculate the total days to complete the project: 5 days (initial period) + 17.5 days (Contractor Q alone) = 22.5 days. Why others are wrong: A — This might result from an incorrect calculation of the remaining work or Bob's time to complete it, possibly rounding errors or computational mistakes. B — This could occur if one incorrectly assumed that Q completed the remaining half of the project in 15 days (half of 30) and added it to 5 days, or if P's individual time was mistakenly chosen. D — This option might be chosen if one incorrectly calculated Q's time for the remaining work (e.g., 7/12 of 30 was miscalculated) or made an error in the initial combined work calculation.

1. Calculate the total work in "engineer-days": 5 engineers * 20 days = 100 engineer-days. 2. Calculate the work done in the first 8 days: 5 engineers * 8 days = 40 engineer-days. 3. Calculate the remaining work: 100 engineer-days (total) - 40 engineer-days (done) = 60 engineer-days. 4. Determine the number of remaining engineers: 5 engineers - 2 engineers = 3 engineers. 5. Calculate the additional days required by the remaining engineers: 60 engineer-days / 3 engineers = 20 days. Why others are wrong: A — Correct answer. B — This would be the remaining days if the original 5 engineers continued without interruption (20 - 8 = 12 days), not accounting for the reduced team size. C — This is the total time from the start of the project (8 initial days + 20 additional days), not just the additional days required. D — This results from incorrectly dividing the remaining work by the number of engineers who *left* (60 engineer-days / 2 engineers = 30 days) instead of the engineers who remained.

1. Calculate Worker A's efficiency: Worker A produces 500 units in 10 hours, so Worker A's rate is 500 units / 10 hours = 50 units/hour. 2. Calculate Worker B's efficiency: Worker B is 25% more efficient than Worker A. So, Worker B's rate is 50 units/hour * 1.25 = 62.5 units/hour. 3. Calculate work done by Worker A in the first 4 hours: 50 units/hour * 4 hours = 200 units. 4. Calculate work done by Worker B in the first 4 hours: 62.5 units/hour * 4 hours = 250 units. 5. Calculate total work done by both workers in the first 4 hours: 200 units (by A) + 250 units (by B) = 450 units. 6. Calculate remaining work: The total target is 1200 units. Remaining work = 1200 units - 450 units = 750 units. 7. Calculate time for Worker B to complete the remaining work alone: Remaining work / Worker B's rate = 750 units / 62.5 units/hour = 12 hours. Why others are wrong: B — This would be the answer if Worker B's efficiency was incorrectly calculated as 50 + 25 = 75 units/hour. C — This would be the answer if Worker B's efficiency was mistakenly taken as Worker A's efficiency (50 units/hour) for the remaining work. D — This represents the total time Worker B worked (4 hours initially + 12 hours alone), not the additional hours required.

1. Calculate Anil's daily work rate: 1/20 of the project. 2. Calculate Bala's daily work rate: 1/30 of the project. 3. Calculate their combined daily work rate: 1/20 + 1/30 = (3/60) + (2/60) = 5/60 = 1/12 of the project per day. 4. Calculate the work done in the first 6 days by Anil and Bala working together: 6 days * (1/12 project/day) = 6/12 = 1/2 of the project. 5. Calculate the remaining work: Total work (1) - Work done (1/2) = 1/2 of the project. 6. Calculate the time Bala needs to complete the remaining work alone: Remaining work / Bala's daily work rate = (1/2) / (1/30) = (1/2) * 30 = 15 days. Why others are wrong: A — This might be the result of miscalculating the remaining work or applying the wrong rate. C — Could result from an arithmetic error or an incorrect assumption about the fraction of work remaining (e.g., if one incorrectly thought 3/5 of the work remained). D — This is Anil's individual time to complete the entire project, not the time for Bala to finish the remaining work.

1. Let the total work be 1 unit. 2. Person Y completes the work in 30 days, so Y's 1-day work rate = 1/30 of the project. 3. Person X is twice as efficient as Y. So, X's 1-day work rate = 2 * (1/30) = 1/15 of the project. (This means X can complete the project alone in 15 days). 4. Combined 1-day work rate of X and Y = (1/15) + (1/30) = (2/30) + (1/30) = 3/30 = 1/10 of the project. 5. Work done by X and Y together in 4 days = 4 * (1/10) = 4/10 = 2/5 of the project. 6. Remaining work = Total work - Work done = 1 - 2/5 = 3/5 of the project. 7. After X leaves, only Y works. Time taken by Y to complete the remaining work = (Remaining work) / (Y's 1-day work rate). 8. Time = (3/5) / (1/30) = (3/5) * 30 = 3 * 6 = 18 days. Why others are wrong: A — This could result from an error in calculating the remaining work (e.g., if remaining work was incorrectly taken as 1/2, then 1/2 * 30 = 15). C — This could arise if the work done together was incorrectly calculated (e.g., if 1/3 of the work was done, remaining 2/3 * 30 = 20). D — This could result from significant errors in efficiency calculations or remaining work calculation (e.g., if 4/5 of the work remained, then 4/5 * 30 = 24).